Subgroups — C₁₃×#61960 #15748299

Order 3328.

1834 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3475	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3398	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3372	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3329	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3312	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3276	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3266	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3252	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3249	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3218	C₂	1	2	yes	maximal, complemented
12	C₁₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3116	C₂	1	2	yes	maximal, complemented
14	C₁₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#3039	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#137	C₂²	1	4	yes	—
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
20	Q₈²×C₁₃	—	2	1	no	—
21	C₁₃×#557	C₂²	1	2	yes	complemented
22	C₁₃×#556	C₂²	1	1	yes	characteristic
23	C₁₃×#555	C₂²	1	1	yes	characteristic
24	C₁₃×#554	—	2	2	no	—
25	C₁₃×#554	—	2	1	no	—
26	C₁₃×#554	C₂²	1	1	yes	characteristic
27	C₁₃×#553	—	2	1	no	—
28	C₁₃×#552	—	2	1	no	—
29	C₁₃×#552	C₂²	1	2	yes	—
30	C₁₃×#551	—	2	2	no	—
31	D₄×Q₈×C₁₃	C₂²	1	4	yes	—
32	D₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
33	C₁₃×#547	C₂²	1	1	yes	characteristic
34	C₁₃×#546	C₂²	1	2	yes	—
35	C₁₃×#544	—	2	1	no	—
36	C₁₃×#544	—	2	2	no	—
37	C₁₃×#533	C₂²	1	1	yes	characteristic
38	C₁₃×#533	C₂²	1	1	yes	characteristic
39	C₁₃×#533	C₂²	1	2	yes	complemented
40	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
42	C₁₃×#529	—	2	2	no	—
43	C₁₃×#529	C₂²	1	2	yes	—
44	C₁₃×#525	—	2	1	no	—
45	C₁₃×#520	—	2	1	no	—
46	C₄×C₁₃×#41	C₂²	1	2	yes	—
47	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#117	—	2	1	no	—
50	C₁₃×#497	C₂²	1	4	yes	—
51	C₁₃×#494	C₂²	1	2	yes	complemented
52	C₁₃×#491	C₂²	1	4	yes	complemented
53	C₁₃×#487	C₂²	1	2	yes	complemented
54	C₁₃×#485	C₂²	1	4	yes	complemented
55	C₁₃×#483	C₂²	1	2	yes	—
56	C₁₃×#479	C₂²	1	4	yes	complemented
57	C₁₃×#477	C₂²	1	2	yes	complemented
58	C₁₃×#477	C₂²	1	2	yes	complemented
59	C₁₃×#476	C₂²	1	1	yes	characteristic
60	C₁₃×#476	C₂²	1	1	yes	characteristic
61	C₁₃×#470	C₂²	1	4	yes	complemented
62	C₁₃×#468	C₂²	1	4	yes	—
63	C₁₃×#467	C₂²	1	4	yes	—
64	C₁₃×#464	C₂²	1	4	yes	—
65	C₁₃×#462	C₂²	1	2	yes	complemented
66	C₁₃×#462	C₂²	1	4	yes	complemented
67	C₁₃×#462	C₂²	1	2	yes	complemented
68	C₁₃×#462	C₂²	1	2	yes	complemented
69	C₁₃×#462	C₂²	1	2	yes	complemented
70	C₁₃×#461	C₂²	1	4	yes	—
71	C₁₃×#461	C₂²	1	2	yes	—
72	C₁₃×#461	C₂²	1	2	yes	—
73	C₁₃×#461	C₂²	1	2	yes	—
74	C₁₃×#461	C₂²	1	2	yes	—
75	C₁₃×#461	C₂²	1	1	yes	characteristic
76	C₁₃×#461	C₂²	1	1	yes	characteristic
77	C₁₃×#452	C₂²	1	4	yes	—
78	C₁₃×#451	C₂²	1	4	yes	—
79	C₁₃×#451	C₂²	1	4	yes	complemented
80	C₁₃×#450	C₂²	1	2	yes	—
81	C₁₃×#448	C₂²	1	4	yes	—
82	C₁₃×#446	C₂²	1	2	yes	complemented
83	C₁₃×#441	C₂²	1	4	yes	complemented
84	C₁₃×#440	C₂²	1	4	yes	—
85	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
86	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
87	C₁₃×#436	C₂²	1	2	yes	complemented
88	C₁₃×#435	C₂²	1	4	yes	—
89	C₁₃×#432	C₂²	1	2	yes	complemented
90	C₁₃×#431	C₂²	1	1	yes	characteristic
91	C₁₃×#423	C₂²	1	2	yes	complemented
92	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
93	C₁₃×#419	C₂²	1	4	yes	complemented
94	C₂×C₁₃×#103	C₂²	1	2	yes	—
95	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
96	C₂×C₁₃×#41	C₂³	1	2	yes	—
97	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
98	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
99	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₁₃	—	2	1	no	—
101	C₁₃×#137	—	4	8	no	—
102	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
103	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
104	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
105	C₂×C₁₃×SD₁₆	—	4	4	no	—
106	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
107	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
108	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
109	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
110	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
111	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
112	C₁₃×C₄⋊Q₈	—	2	4	no	—
113	C₁₃×C₄⋊Q₈	—	2	2	no	—
114	C₁₃×C₄⋊Q₈	—	2	1	no	—
115	C₁₃×C₄⋊Q₈	—	2	1	no	—
116	C₁₃×C₄⋊Q₈	—	2	2	no	—
117	C₁₃×C₄⋊Q₈	—	2	2	no	—
118	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
122	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₁₃×#126	—	2	2	no	—
126	C₁₃×#126	—	2	2	no	—
127	C₁₃×#126	—	2	2	no	—
128	C₁₃×#125	—	2	2	no	—
129	C₁₃×#125	—	2	2	no	—
130	C₁₃×#125	—	2	4	no	—
131	C₁₃×#125	—	2	1	no	—
132	C₁₃×#125	—	2	1	no	—
133	C₁₃×#125	—	2	2	no	—
134	C₁₃×#125	C₂³	1	2	yes	—
135	C₁₃×#124	—	2	2	no	—
136	C₁₃×#124	C₂³	1	2	yes	—
137	C₁₃×#123	—	2	2	no	—
138	C₁₃×#123	—	2	2	no	—
139	C₁₃×#123	—	2	2	no	—
140	C₁₃×#123	—	2	2	no	—
141	C₁₃×C₂²⋊Q₈	—	2	1	no	—
142	C₁₃×C₂²⋊Q₈	—	2	1	no	—
143	C₁₃×C₂²⋊Q₈	—	2	1	no	—
144	C₁₃×C₂²⋊Q₈	—	2	1	no	—
145	C₁₃×C₂²⋊Q₈	—	2	2	no	—
146	C₁₃×C₂²⋊Q₈	—	2	2	no	—
147	C₁₃×C₂²⋊Q₈	—	2	4	no	—
148	C₁₃×C₂²⋊Q₈	—	2	4	no	—
149	C₁₃×C₂²⋊Q₈	—	2	4	no	—
150	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₁₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
154	C₁₃×#121	—	2	1	no	—
155	C₁₃×#121	—	2	1	no	—
156	C₁₃×#121	—	2	2	no	—
157	C₁₃×#121	C₂³	1	2	yes	—
158	C₁₃×#120	—	2	2	no	—
159	C₄×Q₈×C₁₃	—	2	2	no	—
160	C₄×Q₈×C₁₃	—	2	1	no	—
161	C₄×Q₈×C₁₃	—	2	1	no	—
162	C₄×Q₈×C₁₃	—	2	2	no	—
163	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
165	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
166	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
169	C₄×D₄×C₁₃	—	2	4	no	—
170	C₄×D₄×C₁₃	—	2	2	no	—
171	C₄×D₄×C₁₃	—	2	2	no	—
172	C₄×D₄×C₁₃	—	2	2	no	—
173	C₄×D₄×C₁₃	—	2	2	no	—
174	C₄×D₄×C₁₃	—	2	1	no	—
175	C₄×D₄×C₁₃	—	2	1	no	—
176	C₄×D₄×C₁₃	D₄	1	2	yes	—
177	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
178	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₁₃	C₂³	1	2	yes	—
181	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₁₃	C₂³	1	2	yes	—
184	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
185	C₁₃×#117	—	2	1	no	—
186	C₁₃×#117	—	2	1	no	—
187	C₁₃×#117	—	2	2	no	—
188	C₁₃×#117	—	2	1	no	—
189	C₁₃×#117	—	2	1	no	—
190	C₁₃×#117	—	2	2	no	—
191	C₁₃×#117	—	2	2	no	—
192	C₁₃×#117	—	2	2	no	—
193	C₁₃×#117	D₄	1	1	yes	characteristic
194	C₁₃×#117	D₄	1	2	yes	—
195	C₁₃×#117	C₂³	1	2	yes	—
196	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
197	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
200	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
203	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
204	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
205	C₂×C₄²×C₁₃	—	2	2	no	—
206	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
208	C₁₃×#107	C₂³	1	4	yes	—
209	C₁₃×#106	C₂³	1	2	yes	—
210	C₁₃×#106	C₂³	1	2	yes	—
211	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
212	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
215	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₁₃×#103	C₂³	1	4	yes	—
217	C₁₃×#103	C₂³	1	4	yes	—
218	C₁₃×#103	C₂³	1	2	yes	—
219	C₁₃×#103	C₂³	1	4	yes	—
220	C₁₃×#103	C₂³	1	4	yes	—
221	C₁₃×#103	C₂³	1	2	yes	—
222	C₁₃×#103	C₂³	1	4	yes	—
223	C₁₃×#103	C₂³	1	4	yes	—
224	C₁₃×#102	C₂³	1	2	yes	—
225	C₁₃×#102	C₂³	1	2	yes	—
226	C₁₃×C₂²⋊C₈	C₂³	1	2	yes	—
227	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
228	C₁₃×#97	C₂³	1	4	yes	—
229	C₄×C₈×C₁₃	C₂³	1	2	yes	—
230	#61960	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂⁴×C₁₃	—	2	1	no	—
232	C₁₃×#41	—	2	4	no	—
233	C₁₃×#41	—	2	4	no	—
234	C₁₃×#41	—	4	2	no	—
235	C₂×Q₈×C₁₃	—	2	1	no	—
236	C₂×Q₈×C₁₃	—	2	1	no	—
237	C₂×Q₈×C₁₃	—	2	4	no	—
238	C₂×Q₈×C₁₃	—	2	2	no	—
239	C₂×Q₈×C₁₃	—	4	2	no	—
240	C₂×Q₈×C₁₃	—	4	4	no	—
241	C₂×Q₈×C₁₃	—	4	2	no	—
242	C₂×Q₈×C₁₃	—	4	4	no	—
243	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
245	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
247	C₂×D₄×C₁₃	—	2	2	no	—
248	C₂×D₄×C₁₃	—	2	2	no	—
249	C₂×D₄×C₁₃	—	2	2	no	—
250	C₂×D₄×C₁₃	—	2	1	no	—
251	C₂×D₄×C₁₃	—	4	1	no	—
252	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
254	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×D₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₃	—	2	1	no	—
257	C₂²×C₄×C₁₃	—	2	4	no	—
258	C₂²×C₄×C₁₃	—	2	2	no	—
259	C₂²×C₄×C₁₃	—	2	1	no	—
260	C₂²×C₄×C₁₃	—	2	2	no	—
261	C₂²×C₄×C₁₃	—	2	1	no	—
262	C₂²×C₄×C₁₃	—	2	1	no	—
263	C₂²×C₄×C₁₃	—	2	1	no	—
264	C₂²×C₄×C₁₃	—	2	2	no	—
265	C₂²×C₄×C₁₃	—	4	4	no	—
266	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
269	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
272	C₁₃×Q₁₆	—	4	4	no	—
273	C₁₃×Q₁₆	—	4	4	no	—
274	C₁₃×Q₁₆	—	4	4	no	—
275	C₁₃×SD₁₆	—	2	8	no	—
276	C₁₃×SD₁₆	—	2	4	no	—
277	C₁₃×SD₁₆	—	4	4	no	—
278	C₁₃×SD₁₆	—	4	2	no	—
279	C₁₃×M₁₆	—	4	4	no	—
280	C₂×C₈×C₁₃	—	4	2	no	—
281	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
282	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
283	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
284	C₁₃×C₄⋊C₄	—	2	2	no	—
285	C₁₃×C₄⋊C₄	—	2	1	no	—
286	C₁₃×C₄⋊C₄	—	2	2	no	—
287	C₁₃×C₄⋊C₄	—	2	1	no	—
288	C₁₃×C₄⋊C₄	—	2	1	no	—
289	C₁₃×C₄⋊C₄	—	2	1	no	—
290	C₁₃×C₄⋊C₄	—	2	2	no	—
291	C₁₃×C₄⋊C₄	—	2	2	no	—
292	C₁₃×C₄⋊C₄	—	2	4	no	—
293	C₁₃×C₄⋊C₄	—	2	2	no	—
294	C₁₃×C₄⋊C₄	—	2	4	no	—
295	C₁₃×C₄⋊C₄	—	2	2	no	—
296	C₁₃×C₄⋊C₄	—	2	1	no	—
297	C₁₃×C₄⋊C₄	—	2	1	no	—
298	C₁₃×C₄⋊C₄	—	2	2	no	—
299	C₁₃×C₄⋊C₄	—	2	2	no	—
300	C₁₃×C₄⋊C₄	—	2	2	no	—
301	C₁₃×C₄⋊C₄	—	2	2	no	—
302	C₁₃×C₄⋊C₄	—	2	4	no	—
303	C₁₃×C₄⋊C₄	—	2	2	no	—
304	C₁₃×C₄⋊C₄	—	2	1	no	—
305	C₁₃×C₄⋊C₄	—	2	4	no	—
306	C₁₃×C₄⋊C₄	—	2	2	no	—
307	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
308	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
309	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
310	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
311	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
312	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
313	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
314	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
315	C₁₃×C₂²⋊C₄	—	2	2	no	—
316	C₁₃×C₂²⋊C₄	—	2	4	no	—
317	C₁₃×C₂²⋊C₄	—	2	2	no	—
318	C₁₃×C₂²⋊C₄	—	2	2	no	—
319	C₁₃×C₂²⋊C₄	—	2	2	no	—
320	C₁₃×C₂²⋊C₄	—	2	1	no	—
321	C₁₃×C₂²⋊C₄	—	2	2	no	—
322	C₁₃×C₂²⋊C₄	—	2	2	no	—
323	C₁₃×C₂²⋊C₄	—	2	1	no	—
324	C₁₃×C₂²⋊C₄	—	2	1	no	—
325	C₁₃×C₂²⋊C₄	—	2	1	no	—
326	C₁₃×C₂²⋊C₄	—	2	2	no	—
327	C₁₃×C₂²⋊C₄	—	2	2	no	—
328	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
329	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
330	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
331	C₄²×C₁₃	—	2	2	no	—
332	C₄²×C₁₃	—	2	2	no	—
333	C₄²×C₁₃	—	2	2	no	—
334	C₄²×C₁₃	—	2	4	no	—
335	C₄²×C₁₃	—	2	2	no	—
336	C₄²×C₁₃	C₂×D₄	1	2	yes	—
337	C₄²×C₁₃	C₂×D₄	1	2	yes	—
338	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
341	C₄²×C₁₃	C₂⁴	1	2	yes	—
342	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
343	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
344	#3475	C₂×C₁₃	1	1	yes	characteristic
345	#3398	C₂×C₁₃	1	2	yes	complemented
346	#3372	C₂×C₁₃	1	2	yes	complemented
347	#3329	C₂×C₁₃	1	2	yes	complemented
348	#3312	C₂×C₁₃	1	4	yes	complemented
349	#3276	C₂×C₁₃	1	2	yes	complemented
350	#3266	C₂×C₁₃	1	4	yes	complemented
351	#3252	C₂×C₁₃	1	2	yes	complemented
352	#3249	C₂×C₁₃	1	1	yes	characteristic, complemented
353	#3218	C₂×C₁₃	1	2	yes	complemented
354	#3209	C₂×C₁₃	1	1	yes	characteristic, complemented
355	#3116	C₂×C₁₃	1	2	yes	complemented
356	#3101	C₂×C₁₃	1	1	yes	characteristic, complemented
357	#3039	C₂×C₁₃	1	2	yes	complemented
358	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
359	#2989	C₂×C₁₃	1	1	yes	characteristic, complemented
360	C₂³×C₁₃	—	2	1	no	—
361	C₂³×C₁₃	—	2	1	no	—
362	C₂³×C₁₃	—	4	2	no	—
363	C₂³×C₁₃	—	4	2	no	—
364	C₂³×C₁₃	—	8	1	no	—
365	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
366	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
367	Q₈×C₁₃	—	2	2	no	—
368	Q₈×C₁₃	—	2	4	no	—
369	Q₈×C₁₃	—	2	2	no	—
370	Q₈×C₁₃	—	2	2	no	—
371	Q₈×C₁₃	—	2	2	no	—
372	Q₈×C₁₃	—	2	2	no	—
373	Q₈×C₁₃	—	2	4	no	—
374	Q₈×C₁₃	—	4	2	no	—
375	Q₈×C₁₃	—	8	1	no	—
376	Q₈×C₁₃	—	8	4	no	—
377	Q₈×C₁₃	—	8	2	no	—
378	D₄×C₁₃	—	2	4	no	—
379	D₄×C₁₃	—	2	2	no	—
380	D₄×C₁₃	—	2	1	no	—
381	D₄×C₁₃	—	2	1	no	—
382	D₄×C₁₃	—	2	1	no	—
383	D₄×C₁₃	—	4	2	no	—
384	D₄×C₁₃	—	4	4	no	—
385	D₄×C₁₃	—	8	2	no	—
386	D₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
387	C₂×C₄×C₁₃	—	2	4	no	—
388	C₂×C₄×C₁₃	—	2	1	no	—
389	C₂×C₄×C₁₃	—	2	2	no	—
390	C₂×C₄×C₁₃	—	2	1	no	—
391	C₂×C₄×C₁₃	—	2	2	no	—
392	C₂×C₄×C₁₃	—	2	1	no	—
393	C₂×C₄×C₁₃	—	2	2	no	—
394	C₂×C₄×C₁₃	—	2	2	no	—
395	C₂×C₄×C₁₃	—	2	2	no	—
396	C₂×C₄×C₁₃	—	2	4	no	—
397	C₂×C₄×C₁₃	—	2	2	no	—
398	C₂×C₄×C₁₃	—	2	1	no	—
399	C₂×C₄×C₁₃	—	4	2	no	—
400	C₂×C₄×C₁₃	—	4	1	no	—
401	C₂×C₄×C₁₃	—	4	4	no	—
402	C₂×C₄×C₁₃	—	4	2	no	—
403	C₂×C₄×C₁₃	—	4	2	no	—
404	C₂×C₄×C₁₃	—	4	2	no	—
405	C₂×C₄×C₁₃	—	4	2	no	—
406	C₂×C₄×C₁₃	—	4	2	no	—
407	C₂×C₄×C₁₃	—	8	2	no	—
408	C₂×C₄×C₁₃	—	8	2	no	—
409	C₂×C₄×C₁₃	—	8	4	no	—
410	C₂×C₄×C₁₃	#137	1	4	yes	complemented
411	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
420	C₈×C₁₃	—	2	4	no	—
421	C₈×C₁₃	—	2	2	no	—
422	C₈×C₁₃	—	2	2	no	—
423	C₂×#137	C₂²×C₁₃	1	4	yes	—
424	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
425	Q₈²	—	2	1	no	—
426	#557	C₂²×C₁₃	1	2	yes	complemented
427	#556	C₂²×C₁₃	1	1	yes	characteristic
428	#555	C₂²×C₁₃	1	1	yes	characteristic
429	#554	—	2	2	no	—
430	#554	—	2	1	no	—
431	#554	C₂²×C₁₃	1	1	yes	characteristic
432	#553	—	2	1	no	—
433	#552	—	2	1	no	—
434	#552	C₂²×C₁₃	1	2	yes	—
435	#551	—	2	2	no	—
436	D₄×Q₈	C₂²×C₁₃	1	4	yes	—
437	D₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
438	#547	C₂²×C₁₃	1	1	yes	characteristic
439	#546	C₂²×C₁₃	1	2	yes	—
440	#544	—	2	1	no	—
441	#544	—	2	2	no	—
442	#533	C₂²×C₁₃	1	1	yes	characteristic
443	#533	C₂²×C₁₃	1	1	yes	characteristic
444	#533	C₂²×C₁₃	1	2	yes	complemented
445	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
446	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
447	#529	—	2	2	no	—
448	#529	C₂²×C₁₃	1	2	yes	—
449	#525	—	2	1	no	—
450	#520	—	2	1	no	—
451	C₄×#41	C₂²×C₁₃	1	2	yes	—
452	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
453	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
454	C₂×#117	—	2	1	no	—
455	#497	C₂²×C₁₃	1	4	yes	—
456	#494	C₂²×C₁₃	1	2	yes	complemented
457	#491	C₂²×C₁₃	1	4	yes	complemented
458	#487	C₂²×C₁₃	1	2	yes	complemented
459	#485	C₂²×C₁₃	1	4	yes	complemented
460	#483	C₂²×C₁₃	1	2	yes	—
461	#479	C₂²×C₁₃	1	4	yes	complemented
462	#477	C₂²×C₁₃	1	2	yes	complemented
463	#477	C₂²×C₁₃	1	2	yes	complemented
464	#476	C₂²×C₁₃	1	1	yes	characteristic
465	#476	C₂²×C₁₃	1	1	yes	characteristic
466	#470	C₂²×C₁₃	1	4	yes	complemented
467	#468	C₂²×C₁₃	1	4	yes	—
468	#467	C₂²×C₁₃	1	4	yes	—
469	#464	C₂²×C₁₃	1	4	yes	—
470	#462	C₂²×C₁₃	1	2	yes	complemented
471	#462	C₂²×C₁₃	1	2	yes	complemented
472	#462	C₂²×C₁₃	1	4	yes	complemented
473	#462	C₂²×C₁₃	1	2	yes	complemented
474	#462	C₂²×C₁₃	1	2	yes	complemented
475	#461	C₂²×C₁₃	1	2	yes	—
476	#461	C₂²×C₁₃	1	1	yes	characteristic
477	#461	C₂²×C₁₃	1	1	yes	characteristic
478	#461	C₂²×C₁₃	1	2	yes	—
479	#461	C₂²×C₁₃	1	4	yes	—
480	#461	C₂²×C₁₃	1	2	yes	—
481	#461	C₂²×C₁₃	1	2	yes	—
482	#452	C₂²×C₁₃	1	4	yes	—
483	#451	C₂²×C₁₃	1	4	yes	—
484	#451	C₂²×C₁₃	1	4	yes	complemented
485	#450	C₂²×C₁₃	1	2	yes	—
486	#448	C₂²×C₁₃	1	4	yes	—
487	#446	C₂²×C₁₃	1	2	yes	complemented
488	#441	C₂²×C₁₃	1	4	yes	complemented
489	#440	C₂²×C₁₃	1	4	yes	—
490	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
491	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
492	#436	C₂²×C₁₃	1	2	yes	complemented
493	#435	C₂²×C₁₃	1	4	yes	—
494	#432	C₂²×C₁₃	1	2	yes	complemented
495	#431	C₂²×C₁₃	1	1	yes	characteristic
496	#423	C₂²×C₁₃	1	2	yes	complemented
497	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
498	#419	C₂²×C₁₃	1	4	yes	complemented
499	C₂×#103	C₂²×C₁₃	1	2	yes	—
500	C₂²×C₁₃	—	2	1	no	—
501	C₂²×C₁₃	—	2	1	no	—
502	C₂²×C₁₃	—	2	2	no	—
503	C₂²×C₁₃	—	2	2	no	—
504	C₂²×C₁₃	—	2	2	no	—
505	C₂²×C₁₃	—	2	2	no	—
506	C₂²×C₁₃	—	4	1	no	—
507	C₂²×C₁₃	—	4	1	no	—
508	C₂²×C₁₃	—	4	1	no	—
509	C₂²×C₁₃	—	4	1	no	—
510	C₂²×C₁₃	—	4	1	no	—
511	C₂²×C₁₃	—	8	4	no	—
512	C₂²×C₁₃	C₂×#137	1	2	yes	—
513	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
514	C₄×C₁₃	—	2	1	no	—
515	C₄×C₁₃	—	2	2	no	—
516	C₄×C₁₃	—	2	1	no	—
517	C₄×C₁₃	—	2	2	no	—
518	C₄×C₁₃	—	2	1	no	—
519	C₄×C₁₃	—	2	2	no	—
520	C₄×C₁₃	—	4	2	no	—
521	C₄×C₁₃	—	4	2	no	—
522	C₄×C₁₃	—	4	2	no	—
523	C₄×C₁₃	—	4	4	no	—
524	C₄×C₁₃	—	4	2	no	—
525	C₄×C₁₃	—	4	1	no	—
526	C₄×C₁₃	—	4	1	no	—
527	C₄×C₁₃	C₂×#137	1	2	yes	—
528	C₄×C₁₃	C₂×#137	1	2	yes	—
529	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₄×C₁₃	#585	1	1	yes	characteristic
531	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
532	C₂×#41	C₂³×C₁₃	1	2	yes	—
533	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
534	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
535	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
536	C₂³×C₄	—	2	1	no	—
537	#137	—	4	8	no	—
538	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
539	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
540	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
541	C₂×SD₁₆	—	4	4	no	—
542	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
543	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
544	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
545	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
546	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
547	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
548	C₄⋊Q₈	—	2	4	no	—
549	C₄⋊Q₈	—	2	2	no	—
550	C₄⋊Q₈	—	2	1	no	—
551	C₄⋊Q₈	—	2	1	no	—
552	C₄⋊Q₈	—	2	2	no	—
553	C₄⋊Q₈	—	2	2	no	—
554	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
555	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
556	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
557	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
558	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
559	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
560	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
561	#126	—	2	2	no	—
562	#126	—	2	2	no	—
563	#126	—	2	2	no	—
564	#125	—	2	2	no	—
565	#125	—	2	2	no	—
566	#125	—	2	4	no	—
567	#125	—	2	1	no	—
568	#125	—	2	1	no	—
569	#125	—	2	2	no	—
570	#125	C₂³×C₁₃	1	2	yes	—
571	#124	—	2	2	no	—
572	#124	C₂³×C₁₃	1	2	yes	—
573	#123	—	2	2	no	—
574	#123	—	2	2	no	—
575	#123	—	2	2	no	—
576	#123	—	2	2	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	1	no	—
579	C₂²⋊Q₈	—	2	1	no	—
580	C₂²⋊Q₈	—	2	1	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	—	2	2	no	—
583	C₂²⋊Q₈	—	2	4	no	—
584	C₂²⋊Q₈	—	2	4	no	—
585	C₂²⋊Q₈	—	2	4	no	—
586	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
587	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
588	C₂²⋊Q₈	C₂³×C₁₃	1	2	yes	—
589	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
590	#121	—	2	1	no	—
591	#121	—	2	1	no	—
592	#121	—	2	2	no	—
593	#121	C₂³×C₁₃	1	2	yes	—
594	#120	—	2	2	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	2	no	—
599	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
601	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
602	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
603	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
604	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
605	C₄×D₄	—	2	4	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	D₄×C₁₃	1	2	yes	—
613	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
614	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
617	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
618	C₄×D₄	C₂³×C₁₃	1	2	yes	—
619	C₄×D₄	C₂³×C₁₃	1	2	yes	—
620	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
621	#117	—	2	1	no	—
622	#117	—	2	1	no	—
623	#117	—	2	2	no	—
624	#117	—	2	1	no	—
625	#117	—	2	1	no	—
626	#117	—	2	2	no	—
627	#117	—	2	2	no	—
628	#117	—	2	2	no	—
629	#117	D₄×C₁₃	1	1	yes	characteristic
630	#117	D₄×C₁₃	1	2	yes	—
631	#117	C₂³×C₁₃	1	2	yes	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	2	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	2	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	1	no	—
638	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	2	no	—
641	C₂×C₄²	—	2	2	no	—
642	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
644	#107	C₂³×C₁₃	1	4	yes	—
645	#106	C₂³×C₁₃	1	2	yes	—
646	#106	C₂³×C₁₃	1	2	yes	—
647	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
648	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
649	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
650	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
651	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
652	#103	C₂³×C₁₃	1	4	yes	—
653	#103	C₂³×C₁₃	1	4	yes	—
654	#103	C₂³×C₁₃	1	2	yes	—
655	#103	C₂³×C₁₃	1	4	yes	—
656	#103	C₂³×C₁₃	1	4	yes	—
657	#103	C₂³×C₁₃	1	2	yes	—
658	#103	C₂³×C₁₃	1	4	yes	—
659	#103	C₂³×C₁₃	1	4	yes	—
660	#102	C₂³×C₁₃	1	2	yes	—
661	#102	C₂³×C₁₃	1	2	yes	—
662	C₂²⋊C₈	C₂³×C₁₃	1	2	yes	—
663	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
664	#97	C₂³×C₁₃	1	4	yes	—
665	C₄×C₈	C₂³×C₁₃	1	2	yes	—
666	C₂×C₁₃	—	2	2	no	—
667	C₂×C₁₃	—	4	2	no	—
668	C₂×C₁₃	—	4	2	no	—
669	C₂×C₁₃	—	8	1	no	—
670	C₂×C₁₃	#3488	1	1	yes	characteristic
671	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
672	C₂×C₁₃	#3586	1	1	yes	characteristic
673	C₂⁴	—	2	1	no	—
674	#41	—	2	4	no	—
675	#41	—	2	4	no	—
676	#41	—	4	2	no	—
677	C₂×Q₈	—	2	1	no	—
678	C₂×Q₈	—	2	1	no	—
679	C₂×Q₈	—	2	4	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	4	2	no	—
682	C₂×Q₈	—	4	4	no	—
683	C₂×Q₈	—	4	2	no	—
684	C₂×Q₈	—	4	4	no	—
685	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
686	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
687	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
688	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	1	no	—
693	C₂×D₄	—	4	1	no	—
694	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
695	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
696	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
697	C₂×D₄	C₂⁴×C₁₃	1	1	yes	characteristic
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	4	4	no	—
708	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
709	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
711	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
712	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
714	Q₁₆	—	4	4	no	—
715	Q₁₆	—	4	4	no	—
716	Q₁₆	—	4	4	no	—
717	SD₁₆	—	2	8	no	—
718	SD₁₆	—	2	4	no	—
719	SD₁₆	—	4	4	no	—
720	SD₁₆	—	4	2	no	—
721	M₁₆	—	4	4	no	—
722	C₂×C₈	—	4	2	no	—
723	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
724	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
725	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	1	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	1	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
750	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
751	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
752	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
753	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
754	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
755	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
756	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	1	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	1	no	—
767	C₂²⋊C₄	—	2	1	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
771	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
772	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	2	no	—
778	C₄²	C₂×D₄×C₁₃	1	2	yes	—
779	C₄²	C₂×D₄×C₁₃	1	2	yes	—
780	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
781	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
782	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
783	C₄²	C₂⁴×C₁₃	1	2	yes	—
784	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
785	C₁₃	#61960	1	1	yes	characteristic, direct product factor, Sylow
786	C₂³	—	2	1	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	4	2	no	—
789	C₂³	—	4	2	no	—
790	C₂³	—	8	1	no	—
791	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
792	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
793	Q₈	—	2	2	no	—
794	Q₈	—	2	4	no	—
795	Q₈	—	2	2	no	—
796	Q₈	—	2	2	no	—
797	Q₈	—	2	2	no	—
798	Q₈	—	2	2	no	—
799	Q₈	—	2	4	no	—
800	Q₈	—	4	2	no	—
801	Q₈	—	8	4	no	—
802	Q₈	—	8	2	no	—
803	Q₈	—	8	1	no	—
804	D₄	—	2	4	no	—
805	D₄	—	2	2	no	—
806	D₄	—	2	1	no	—
807	D₄	—	2	1	no	—
808	D₄	—	2	1	no	—
809	D₄	—	4	2	no	—
810	D₄	—	4	4	no	—
811	D₄	—	8	2	no	—
812	D₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
813	C₂×C₄	—	2	4	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	4	2	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	4	2	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	8	2	no	—
834	C₂×C₄	—	8	2	no	—
835	C₂×C₄	—	8	4	no	—
836	C₂×C₄	C₁₃×#137	1	4	yes	complemented
837	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
838	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
839	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
840	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
841	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
842	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
843	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
844	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
845	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
846	C₈	—	2	4	no	—
847	C₈	—	2	2	no	—
848	C₈	—	2	2	no	—
849	C₂²	—	2	1	no	—
850	C₂²	—	2	1	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	2	no	—
854	C₂²	—	2	2	no	—
855	C₂²	—	4	1	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	1	no	—
858	C₂²	—	4	1	no	—
859	C₂²	—	4	1	no	—
860	C₂²	—	8	4	no	—
861	C₂²	C₂×C₁₃×#137	1	2	yes	—
862	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
863	C₄	—	2	2	no	—
864	C₄	—	2	1	no	—
865	C₄	—	2	2	no	—
866	C₄	—	2	1	no	—
867	C₄	—	2	2	no	—
868	C₄	—	2	1	no	—
869	C₄	—	4	1	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	4	no	—
875	C₄	—	4	2	no	—
876	C₄	C₂×C₁₃×#137	1	2	yes	—
877	C₄	C₂×C₁₃×#137	1	2	yes	—
878	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
879	C₄	C₁₃×#585	1	1	yes	characteristic
880	C₂	—	2	2	no	—
881	C₂	—	4	2	no	—
882	C₂	—	4	2	no	—
883	C₂	—	8	1	no	—
884	C₂	C₁₃×#3488	1	1	yes	characteristic
885	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
886	C₂	C₁₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3475	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3398	C₂	semidirect
4. C₁₃×#3372	C₂	semidirect
5. C₁₃×#3329	C₂	semidirect
6. C₁₃×#3312	C₂	semidirect
7. C₁₃×#3276	C₂	semidirect
8. C₁₃×#3266	C₂	semidirect
9. C₁₃×#3252	C₂	semidirect
10. C₁₃×#3249	C₂	semidirect
11. C₁₃×#3218	C₂	semidirect
12. C₁₃×#3209	C₂	semidirect
13. C₁₃×#3116	C₂	semidirect
14. C₁₃×#3101	C₂	semidirect
15. C₁₃×#3039	C₂	semidirect
16. C₂×C₁₃×#461	C₂	semidirect
17. C₁₃×#2989	C₂	semidirect
21. C₁₃×#557	C₂²	semidirect
32. D₄×Q₈×C₁₃	C₂²	semidirect
39. C₁₃×#533	C₂²	semidirect
41. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
51. C₁₃×#494	C₂²	semidirect
52. C₁₃×#491	C₂²	semidirect
53. C₁₃×#487	C₂²	semidirect
54. C₁₃×#485	C₂²	semidirect
56. C₁₃×#479	C₂²	semidirect
57. C₁₃×#477	C₂²	semidirect
58. C₁₃×#477	C₂²	semidirect
61. C₁₃×#470	C₂²	semidirect
65. C₁₃×#462	C₂²	semidirect
66. C₁₃×#462	C₂²	semidirect
67. C₁₃×#462	C₂²	semidirect
68. C₁₃×#462	C₂²	semidirect
69. C₁₃×#462	C₂²	semidirect
79. C₁₃×#451	C₂²	semidirect
82. C₁₃×#446	C₂²	semidirect
83. C₁₃×#441	C₂²	semidirect
87. C₁₃×#436	C₂²	semidirect
89. C₁₃×#432	C₂²	semidirect
91. C₁₃×#423	C₂²	semidirect
93. C₁₃×#419	C₂²	semidirect
230. #61960	C₁₃	direct (N × H)
343. #3503	C₂×C₁₃	semidirect
345. #3398	C₂×C₁₃	semidirect
346. #3372	C₂×C₁₃	semidirect
347. #3329	C₂×C₁₃	semidirect
348. #3312	C₂×C₁₃	semidirect
349. #3276	C₂×C₁₃	semidirect
350. #3266	C₂×C₁₃	semidirect
351. #3252	C₂×C₁₃	semidirect
352. #3249	C₂×C₁₃	semidirect
353. #3218	C₂×C₁₃	semidirect
354. #3209	C₂×C₁₃	semidirect
355. #3116	C₂×C₁₃	semidirect
356. #3101	C₂×C₁₃	semidirect
357. #3039	C₂×C₁₃	semidirect
358. C₂×#461	C₂×C₁₃	semidirect
359. #2989	C₂×C₁₃	semidirect
410. C₂×C₄×C₁₃	#137	semidirect
426. #557	C₂²×C₁₃	semidirect
437. D₄×Q₈	C₂²×C₁₃	semidirect
444. #533	C₂²×C₁₃	semidirect
446. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
456. #494	C₂²×C₁₃	semidirect
457. #491	C₂²×C₁₃	semidirect
458. #487	C₂²×C₁₃	semidirect
459. #485	C₂²×C₁₃	semidirect
461. #479	C₂²×C₁₃	semidirect
462. #477	C₂²×C₁₃	semidirect
463. #477	C₂²×C₁₃	semidirect
466. #470	C₂²×C₁₃	semidirect
470. #462	C₂²×C₁₃	semidirect
471. #462	C₂²×C₁₃	semidirect
472. #462	C₂²×C₁₃	semidirect
473. #462	C₂²×C₁₃	semidirect
474. #462	C₂²×C₁₃	semidirect
484. #451	C₂²×C₁₃	semidirect
487. #446	C₂²×C₁₃	semidirect
488. #441	C₂²×C₁₃	semidirect
492. #436	C₂²×C₁₃	semidirect
494. #432	C₂²×C₁₃	semidirect
496. #423	C₂²×C₁₃	semidirect
498. #419	C₂²×C₁₃	semidirect
785. C₁₃	#61960	direct (N × H)
836. C₂×C₄	C₁₃×#137	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3503	2
C₁₃×#3475	2
C₁₃×#3398	2
C₁₃×#3372	2
C₁₃×#3329	2
C₁₃×#3312	2
C₁₃×#3276	2
C₁₃×#3266	2
C₁₃×#3252	2
C₁₃×#3249	2
C₁₃×#3218	2
C₁₃×#3209	2
C₁₃×#3116	2
C₁₃×#3101	2
C₁₃×#3039	2
C₂×C₁₃×#461	2
C₁₃×#2989	2
#61960	13

Subgroups — C13×#61960 #15748299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61960 #15748299